Making the Blender Grid round
As mentioned in the comments, there is no way to change the grid pattern in Blender. A workaround to this would be to add a circle curve to guide you.



This process will convert the circle curve to a mesh, meaning it will have vertices like a normal mesh would, as seen in the screenshot below:


From there you can enable vert snapping to align your object to the circle:


As you notice, not all the spheres will align with the center on the vertices, to change this, you have to change the "nearest" option to "center" like so:


Edit
Asker requested this as a half-circle. This is easily achieved by simply cutting the circle in half.


Hope this helps.